Extension of functions with bounded finite differences
classification
🧮 math.DG
keywords
finitedifferencesboundedboundsextensionfunctionstorusdefined
read the original abstract
We prove that functions defined on a lattice in a finite dimensional torus with bounded finite differences can be smoothly extended to the whole torus, and relate the bounds on the extension's derivatives with bounds on the original function's finite differences.
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